Power and magnetism

If we have a solenoid and a magnetic passes through it , it will produce a dc voltage in the wire . If we want to calculate the power , we find out the current using ohms law then we use P=VI . I know there is power loss due to the resistance ( joule effect) . But what about the opposing magnetic field due to current in the wires (lenz's law) , does it contribute in the power loss ?

if you have a stationary coil and a magnet " MOVING" through that coil you don't get dc but AC.
If you would look at an oscilloscope you would see a one half of a sine wave.
If you would continue to push the magnet back and forth at a fixed speed you would get a sine wave output.

The back EMF due to the induced current it pushes against the magnet so to speak so it will get harder for you to push that magnet through.
The faster you will try to push the magnet the harder it will become to do that.You will need to supply a greater force to the magnet which will equal in greater current induced.

There really isn't a loss of power. The amount of power required to push the magnet through will be equal to the total amount of power generated in the coil. However, due to the resistance of the wire, some of the power will be used to heat the wire instead of performing useful work. The opposing magnetic field doesn't cause a loss of power. Instead it is a requirement in order to conserve energy. Without the opposing magnetic field it wouldn't require any work to move the magnet through the coil and you would be creating energy from nothing.